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An invitation to q-series : from Jacobi's triple product identity to Ramanujan's "most beautiful identity" /
The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction -- a result that convinced G H Hardy that Ramanujan was a...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific Pub Co.,
©2011.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Chan, Hei-Chi. | |
| 245 | 1 | 3 | |a An invitation to q-series : |b from Jacobi's triple product identity to Ramanujan's "most beautiful identity" / |c Hei-Chi Chan. |
| 260 | |a Singapore : |b World Scientific Pub Co., |c ©2011. | ||
| 300 | |a 1 online resource (ix, 226 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 504 | |a Includes appendices, bibliographical references (pages 213-223), and index. | ||
| 505 | 0 | |a Introduction -- Part I: Jacobi's triple product identity ; First proof (via functional equation) -- Second proof (via Gaussian polynomials and the q-binomial theorem) -- Some applications -- The Boson-Fermion correspondence -- Macdonald's identities -- Part II: The Rogers-Ramanujan identitites ; First proof (via functional equation) -- Second proof (involving Gaussian polynomials and difference equations) -- Third proof (via Bailey's lemma) -- Excursus : mock theta functions -- Part III: The Rogers-Ramanujan continued fraction ; A list of theorems to be proven -- The evaluation of the Rogers-Ramanujan continued fraction -- A "difficult and deep" identity -- A remarkable identity from the Lost Notebook and cranks -- A differential equation for the Rogers-Ramanujan continued fraction -- Part IV: From the "most beautiful identity" to Ramanujan's congruences ; Proofs of the "most beautiful identity" -- Ramanujan's congruences I : analytical methods -- Ramanujan's congruences II : an introduction to t -cores -- Ramanujan's congruences III : more congruences -- Excursus : modular forms and more congruences for the partition function. | |
| 520 | |a The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction -- a result that convinced G H Hardy that Ramanujan was a "mathematician of the highest class", and (2) what G.H. Hardy called Ramanujan's "Most Beautiful Identity". This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a q-series. | |
| 650 | 0 | |a Jacobi identity. | |
| 650 | 0 | |a Rogers-Ramanujan identities. | |
| 650 | 6 | |a Séries Q. | |
| 650 | 6 | |a Identité de Jacobi. | |
| 650 | 6 | |a Identités de Rogers-Ramanujan. | |
| 650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
| 650 | 7 | |a Jacobi identity |2 fast | |
| 650 | 7 | |a q-series |2 fast | |
| 650 | 7 | |a Rogers-Ramanujan identities |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Chan, Hei-Chi. |t Invitation to q-series. |d Singapore : World Scientific Pub Co., ©2011 |z 9789814343848 |w (DLC) 2011292543 |w (OCoLC)707965406 |
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